Robitaille picked off a clearing attempt on the left side and launched a 45-foot slap shot that got past a screened Ryan Miller to give the Islanders their first win at home since Dec. 26. They were 0-3-1 since.
Andy Hilbert added an insurance goal with 53.9 seconds left.
Arron Asham scored twice and Trent Hunter also scored for the Islanders, while Rick DiPietro, yanked after allowing three goals on five shots Friday night in Atlanta, made 25 saves for the win.
It was just the third time this season New York won when trailing after two periods (3-9-0).
Jochen Hecht scored twice for the Sabres, while Ales Kotalik added a goal. Buffalo lost its third straight game for the first time all season. Miller stopped 26 shots.
The Sabres had previously beaten the Islanders six consecutive times, dating back to a 4-2 home loss on Feb. 27, 2004.
Hunter opened the scoring at 7:42 of the opening period. He took a loose puck in the Buffalo zone, moved down the right boards, avoided a check, got around another player as he maneuvered into the lower right circle and beat Miller to the far side with a low backhand.
Hecht tied the game at 15:01, shortly after the Sabres killed a penalty. Hecht picked up a loose rebound at the left crease, and with DiPietro down in a pileup, backhanded it home.
Miller preserved the tie with 3:51 left in the period with a dazzling rising glove save on Andy Hilbert's point-blank one-timer from the low slot.
Asham put New York ahead 2-1 on a one-timer at 3:03 of the second period, as he converted on a cross-ice feed from Richard Park.
Hecht tied the score with a power-play goal at 5:00. Nathan Paetsch's point shot was saved by DiPietro, but Hecht tipped the rebound off the right post. DiPietro, trying to reach behind him to snare the airborne puck, instead knocked it in with his glove.
Kotalik put the Sabres ahead for the first time at 12:25. His redirection of a pass hit off the right post, and just tucked under the crossbar. The goal survived a video review.
It was Kotalik's 14th goal this season, but just his first in seven games.
Asham tied the score at 6:53 of the final period. He fired a slap shot just inside the blue-line that hit Miller's pads and dribbled through.
Asham has never picked up a hat trick, and this was the fifth time in his career he had a two-goal game.
Notes: Islanders defenceman Brendan Witt missed the game with a hand injury. Allan Rourke was recalled from Bridgeport to take his place. ... The Islanders wore throwback jerseys in a nod to their debut in 1972. The jerseys were a royal blue, with muted orange and white stripes, and orange numbers on the back and sleeves. Also, between faceoffs, there was no canned music just organ music.